Abstract
In this paper, we investigate predictions of the SO(10) Grand Unified Theory (GUT), where an extra U(1)′ gauge symmetry remains up to the supersymmetry (SUSY) breaking scale. The minimal setup of SO(10) GUT unifies quarks and leptons into a 16-representational field in each generations. The setup, however, suffers from the realization of the realistic Yukawa couplings at the electroweak scale. In order to solve this problem, we introduce 10-representational matter fields, and then the two kinds of matter fields mix with each other at the SUSY breaking scale, where the extra U(1)′ gauge symmetry breaks down radiatively. One crucial prediction is that the Standard Model quarks and leptons are given by the linear combinations of the fields with two different U(1)′ charges. The mixing also depends on the flavor. Consequently, the U(1)′ interaction becomes flavor violating, and the flavor physics is the smoking-gun signal of our GUT model. The flavor violating Z′ couplings are related to the fermion masses and the CKM matrix, so that we can derive some explicit predictions in flavor physics. We especially discuss K-\( \overline{K} \) mixing, B (s)-\( \overline{B_{(s)}} \) mixing, and the (semi)leptonic decays of K and B in our model. We also study the flavor violating μ and τ decays and discuss the correlations among the physical observables in this SO(10) GUT framework.
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References
H. Georgi, The state of the art-gauge theories, AIP Conf. Proc. 23 (1975) 575.
H. Fritzsch and P. Minkowski, Unified interactions of leptons and hadrons, Annals Phys. 93 (1975) 193 [INSPIRE].
H. Georgi and C. Jarlskog, A new lepton-quark mass relation in a unified theory, Phys. Lett. B 86 (1979) 297 [INSPIRE].
J.R. Ellis and M.K. Gaillard, Fermion masses and Higgs representations in SU(5), Phys. Lett. B 88 (1979) 315 [INSPIRE].
G. Lazarides, Q. Shafi and C. Wetterich, Proton lifetime and fermion masses in an SO(10) model, Nucl. Phys. B 181 (1981) 287 [INSPIRE].
S.M. Barr, An SO(10) model of fermion masses, Phys. Rev. D 24 (1981) 1895 [INSPIRE].
N. Arkani-Hamed and S. Dimopoulos, Supersymmetric unification without low energy supersymmetry and signatures for fine-tuning at the LHC, JHEP 06 (2005) 073 [hep-th/0405159] [INSPIRE].
G.F. Giudice and A. Romanino, Split supersymmetry, Nucl. Phys. B 699 (2004) 65 [Erratum ibid. B 706 (2005) 487] [hep-ph/0406088] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos, G.F. Giudice and A. Romanino, Aspects of split supersymmetry, Nucl. Phys. B 709 (2005) 3 [hep-ph/0409232] [INSPIRE].
J.D. Wells, PeV-scale supersymmetry, Phys. Rev. D 71 (2005) 015013 [hep-ph/0411041] [INSPIRE].
G.F. Giudice and A. Strumia, Probing high-scale and split supersymmetry with Higgs mass measurements, Nucl. Phys. B 858 (2012) 63 [arXiv:1108.6077] [INSPIRE].
L.J. Hall and Y. Nomura, Spread supersymmetry, JHEP 01 (2012) 082 [arXiv:1111.4519] [INSPIRE].
M. Ibe and T.T. Yanagida, The lightest Higgs boson mass in pure gravity mediation model, Phys. Lett. B 709 (2012) 374 [arXiv:1112.2462] [INSPIRE].
M. Ibe, S. Matsumoto and T.T. Yanagida, Pure gravity mediation with m 3/2 = 10–100 TeV, Phys. Rev. D 85 (2012) 095011 [arXiv:1202.2253] [INSPIRE].
N. Arkani-Hamed, A. Gupta, D.E. Kaplan, N. Weiner and T. Zorawski, Simply unnatural supersymmetry, arXiv:1212.6971 [INSPIRE].
H. Abe, T. Kobayashi and Y. Omura, Relaxed fine-tuning in models with non-universal gaugino masses, Phys. Rev. D 76 (2007) 015002 [hep-ph/0703044] [INSPIRE].
H. Abe, J. Kawamura and H. Otsuka, The Higgs boson mass in a natural MSSM with nonuniversal gaugino masses at the GUT scale, PTEP 2013 (2013) 013B02 [arXiv:1208.5328] [INSPIRE].
J.L. Feng and D. Sanford, A natural 125 GeV Higgs boson in the MSSM from focus point supersymmetry with A-terms, Phys. Rev. D 86 (2012) 055015 [arXiv:1205.2372] [INSPIRE].
H. Baer, V. Barger, P. Huang, A. Mustafayev and X. Tata, Radiative natural SUSY with a 125 GeV Higgs boson, Phys. Rev. Lett. 109 (2012) 161802 [arXiv:1207.3343] [INSPIRE].
J. Hisano, Y. Muramatsu, Y. Omura and M. Yamanaka, Flavor violating Z′ from SO(10) SUSY GUT in High-Scale SUSY, Phys. Lett. B 744 (2015) 395 [arXiv:1503.06156] [INSPIRE].
J. Hisano, D. Kobayashi and N. Nagata, Enhancement of Proton Decay Rates in Supersymmetric SU(5) Grand Unified Models, Phys. Lett. B 716 (2012) 406 [arXiv:1204.6274] [INSPIRE].
J. Hisano, D. Kobayashi, Y. Muramatsu and N. Nagata, Two-loop renormalization factors of dimension-six proton decay operators in the supersymmetric standard models, Phys. Lett. B 724 (2013) 283 [arXiv:1302.2194] [INSPIRE].
J. Hisano, T. Kuwahara and Y. Omura, Threshold corrections to baryon number violating operators in supersymmetric SU(5) GUTs, Nucl. Phys. B 898 (2015) 1 [Erratum ibid. B 907 (2016) 476] [arXiv:1503.08561] [INSPIRE].
B. Bajc, J. Hisano, T. Kuwahara and Y. Omura, Threshold corrections to dimension-six proton decay operators in non-minimal SUSY SU(5) GUTs, Nucl. Phys. B 910 (2016) 1 [arXiv:1603.03568] [INSPIRE].
K.G. Chetyrkin, J.H. Kuhn and M. Steinhauser, RunDec: a Mathematica package for running and decoupling of the strong coupling and quark masses, Comput. Phys. Commun. 133 (2000) 43 [hep-ph/0004189] [INSPIRE].
H. Arason et al., Renormalization group study of the standard model and its extensions. 1. The standard model, Phys. Rev. D 46 (1992) 3945 [INSPIRE].
S.P. Martin and M.T. Vaughn, Regularization dependence of running couplings in softly broken supersymmetry, Phys. Lett. B 318 (1993) 331 [hep-ph/9308222] [INSPIRE].
Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
CKMfitter group, http://ckmfitter.in2p3.fr/www/results/plots_eps15/num/ckmEval_results_eps15.html.
A.J. Buras, F. De Fazio and J. Girrbach, The anatomy of Z′ and Z with flavour changing neutral currents in the flavour precision era, JHEP 02 (2013) 116 [arXiv:1211.1896] [INSPIRE].
J. Laiho, E. Lunghi and R.S. Van de Water, Lattice QCD inputs to the CKM unitarity triangle analysis, Phys. Rev. D 81 (2010) 034503 [arXiv:0910.2928] [INSPIRE], latest values at http://www.latticeaverages.org.
J. Brod and M. Gorbahn, Next-to-next-to-leading-order charm-quark contribution to the CP-violation parameter ϵ K and ΔM K , Phys. Rev. Lett. 108 (2012) 121801 [arXiv:1108.2036] [INSPIRE].
A.J. Buras, M. Jamin and P.H. Weisz, Leading and Next-to-leading QCD corrections to ϵ parameter and B 0 - \( {\overline{B}}^0 \) mixing in the presence of a heavy top quark, Nucl. Phys. B 347 (1990) 491 [INSPIRE].
J. Brod and M. Gorbahn, ϵ K at next-to-next-to-leading order: the charm-top-quark contribution, Phys. Rev. D 82 (2010) 094026 [arXiv:1007.0684] [INSPIRE].
J. Charles, S. Descotes-Genon, Z. Ligeti, S. Monteil, M. Papucci and K. Trabelsi, Future sensitivity to new physics in B d , B s and K mixings, Phys. Rev. D 89 (2014) 033016 [arXiv:1309.2293] [INSPIRE].
Fermilab Lattice, MILC collaboration, A. Bazavov et al., B 0(s) -mixing matrix elements from lattice QCD for the standard model and beyond, Phys. Rev. D 93 (2016) 113016 [arXiv:1602.03560] [INSPIRE].
E391a collaboration, J.K. Ahn et al., Experimental study of the decay \( {K}_L^0\to {\pi}^0\nu \overline{\nu} \), Phys. Rev. D 81 (2010) 072004 [arXiv:0911.4789] [INSPIRE].
BNL-E949 collaboration, A.V. Artamonov et al., Study of the decay \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) in the momentum region 140 < P π z < 199 MeV/c, Phys. Rev. D 79 (2009) 092004 [arXiv:0903.0030] [INSPIRE].
A.J. Buras, D. Buttazzo, J. Girrbach-Noe and R. Knegjens, \( {K}^{+}\to {\pi}^{+}\nu \overline{\nu} \) and \( {K}_L\to {\pi}^0\nu \overline{\nu} \) in the Standard Model: status and perspectives, JHEP 11 (2015) 033 [arXiv:1503.02693] [INSPIRE].
F. Mescia and C. Smith, Improved estimates of rare K decay matrix-elements from Kl3 decays, Phys. Rev. D 76 (2007) 034017 [arXiv:0705.2025] [INSPIRE].
J. Brod, M. Gorbahn and E. Stamou, Two-loop electroweak corrections for the \( K\to \pi \nu \overline{\nu} \) decays, Phys. Rev. D 83 (2011) 034030 [arXiv:1009.0947] [INSPIRE].
G. Isidori and R. Unterdorfer, On the short distance constraints from K L,S → μ + μ −, JHEP 01 (2004) 009 [hep-ph/0311084] [INSPIRE].
A.J. Buras, R. Fleischer, S. Recksiegel and F. Schwab, Anatomy of prominent B and K decays and signatures of CP-violating new physics in the electroweak penguin sector, Nucl. Phys. B 697 (2004) 133 [hep-ph/0402112] [INSPIRE].
M. Gorbahn and U. Haisch, Charm quark contribution to K L → μ + μ − at next-to-next-to-leading, Phys. Rev. Lett. 97 (2006) 122002 [hep-ph/0605203] [INSPIRE].
BNL collaboration, D. Ambrose et al., New limit on muon and electron lepton number violation from K 0 L → μ ± e ∓ decay, Phys. Rev. Lett. 81 (1998) 5734 [hep-ex/9811038] [INSPIRE].
KTeV collaboration, A. Alavi-Harati et al., Search for the rare decay K L → π 0 e + e −, Phys. Rev. Lett. 93 (2004) 021805 [hep-ex/0309072] [INSPIRE].
KTEV collaboration, A. Alavi-Harati et al., Search for the Decay K L → π 0 μ + μ −, Phys. Rev. Lett. 84 (2000) 5279 [hep-ex/0001006] [INSPIRE].
F. Mescia, C. Smith and S. Trine, K L → π 0 e + e − and K L → π 0 μ + μ − : a binary star on the stage of flavor physics, JHEP 08 (2006) 088 [hep-ph/0606081] [INSPIRE].
KTeV collaboration, E. Abouzaid et al., Search for lepton flavor violating decays of the neutral kaon, Phys. Rev. Lett. 100 (2008) 131803 [arXiv:0711.3472] [INSPIRE].
LHCb, CMS collaboration, Observation of the rare B 0 s → μ + μ − decay from the combined analysis of CMS and LHCb data, Nature 522 (2015) 68 [arXiv:1411.4413] [INSPIRE].
C. Bobeth, M. Gorbahn, T. Hermann, M. Misiak, E. Stamou and M. Steinhauser, B s,d → l + l − in the standard model with reduced theoretical uncertainty, Phys. Rev. Lett. 112 (2014) 101801 [arXiv:1311.0903] [INSPIRE].
G. Buchalla and A.J. Buras, The rare decays \( K\to \pi \nu \overline{\nu} \) , \( B\to X\nu \overline{\nu} \) and B → l + l − : an update, Nucl. Phys. B 548 (1999) 309 [hep-ph/9901288] [INSPIRE].
SINDRUM collaboration, U. Bellgardt et al., Search for the decay μ + → e + e + e −, Nucl. Phys. B 299 (1988) 1 [INSPIRE].
A. Blondel et al., Research proposal for an experiment to search for the decay μ → eee, arXiv:1301.6113 [INSPIRE].
R. Kitano, M. Koike and Y. Okada, Detailed calculation of lepton flavor violating muon electron conversion rate for various nuclei, Phys. Rev. D 66 (2002) 096002 [Erratum ibid. D 76 (2007) 059902] [hep-ph/0203110] [INSPIRE].
SINDRUM II collaboration, W.H. Bertl et al., A search for muon to electron conversion in muonic gold, Eur. Phys. J. C 47 (2006) 337 [INSPIRE].
COMET collaboration, Y. Kuno, A search for muon-to-electron conversion at J-PARC: the COMET experiment, PTEP 2013 (2013) 022C01 [INSPIRE].
COMET collaboration, http://comet.kek.jp/Documents_files/IPNS-Review-2014.pdf.
P. Langacker and M. Plümacher, Flavor changing effects in theories with a heavy Z′ boson with family nonuniversal couplings, Phys. Rev. D 62 (2000) 013006 [hep-ph/0001204] [INSPIRE].
K. Hayasaka et al., Search for lepton flavor violating τ decays into three leptons with 719 million produced τ + τ − pairs, Phys. Lett. B 687 (2010) 139 [arXiv:1001.3221] [INSPIRE].
DeeMe collaboration, H. Natori, DeeMe experiment — An experimental search for a μ-e conversion reaction at J-PARC MLF, Nucl. Phys. Proc. Suppl. 248-250 (2014) 52 [INSPIRE].
Mu2e collaboration, Proposal to search for μ − + N → e − N with a single-event sensitivity below 10−16, FERMILAB-PROPOSAL-0973 (2008).
PRISM collaboration, An exprimental search for a μ − -e − conversion at sensitivity of the order of 10−18 with a highly intense muon sourse, http://www-ps.kek.jp/jhf-np/LOIlist/pdf/L25.pdf (2003).
RBC, UKQCD collaboration, Z. Bai et al., Standard model prediction for direct CP-violation in K → ππ decay, Phys. Rev. Lett. 115 (2015) 212001 [arXiv:1505.07863] [INSPIRE].
A.J. Buras, M. Gorbahn, S. Jäger and M. Jamin, Improved anatomy of ϵ′/ϵ in the standard model, JHEP 11 (2015) 202 [arXiv:1507.06345] [INSPIRE].
LHCb collaboration, Measurement of form-factor-independent observables in the decay B 0 → K ∗ 0 μ + μ −, Phys. Rev. Lett. 111 (2013) 191801 [arXiv:1308.1707] [INSPIRE].
LHCb collaboration, Test of lepton universality using B + → K + ℓ + ℓ − decays, Phys. Rev. Lett. 113 (2014) 151601 [arXiv:1406.6482] [INSPIRE].
S. Descotes-Genon, J. Matias and J. Virto, Understanding the B → K * μ + μ − anomaly, Phys. Rev. D 88 (2013) 074002 [arXiv:1307.5683] [INSPIRE].
W. Altmannshofer and D.M. Straub, New physics in b → s transitions after LHC run 1, Eur. Phys. J. C 75 (2015) 382 [arXiv:1411.3161] [INSPIRE].
S. Descotes-Genon, L. Hofer, J. Matias and J. Virto, Global analysis of b → sℓℓ anomalies, JHEP 06 (2016) 092 [arXiv:1510.04239] [INSPIRE].
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Hisano, J., Muramatsu, Y., Omura, Y. et al. Flavor physics induced by light Z′ from SO(10) GUT. J. High Energ. Phys. 2016, 18 (2016). https://doi.org/10.1007/JHEP11(2016)018
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DOI: https://doi.org/10.1007/JHEP11(2016)018